1. Field of the Invention
This invention relates to a sub-band encoding method and apparatus and a sub-band decoding method and apparatus. More particularly, it relates to an encoding method and apparatus in which digital signals, such as digital audio or video signals, are encoded subsequent to spectrum splitting, and a decoding method and apparatus for decoding the encoded signals.
2. Description of the Related Art
Among the encoding/decoding methods for compressing digital signals, there is a sub-band encoding in which the digital signals are split in frequency by a filter for wavelet transform for compressing the digital signals. That is, sub-band coding filters the input signal by plural filters having different pass bands and down-samples the signal at an interval corresponding to the frequency band for compressing the signal by taking advantage of the energy deviation in the filter output signals.
Discussions on sub-band encoding and signal processing by band splitting employing wavelet transform may be found in Martin Vetterli, "Wavelet Transform and Sub-band Encoding", in Journal of Electronic Information Communication Society, vol.74, No.12, pp 1275 to 1278, December 1991.
In general, wavelet transform is said to be a lower-level concept or improvement of sub-band encoding. In the present invention, the wavelet transform is intended to mean not only the filter for wavelet transform itself but also the techniques employing a filter used for sub-band encoding in general.
FIG. 1 shows a basic arrangement for frequency spectrum splitting and synthesis by a filter for wavelet transform. This figure is the same as that shown in the above publication by M. Vetterli. An input signal is a first-order signal xi!.
A splitting unit 100 is a main part of an encoder, while a synthesis unit 110 is a main part of a decoder. In the splitting unit 100, an analysis low-pass filter (LPF) 101.sub.L is an analysis LPF for spectrum splitting, while an analysis high-pass filter (HPF) 101.sub.H is an analysis HPF for frequency splitting. By these two filters 101.sub.L, 101.sub.H, the input signal xi! is split into a low-frequency band signal XLi! and a high-frequency band signal XHi!. Down-sampling units 102.sub.L, 102.sub.H perform sample-based decimation on the band-split signals XLi!, XHi! for generating an output signal XLj!, XHj!, as indicated by the equations 1 and 2: EQU XLj!=XLi!(j=i/2) (1) EQU XHj!=XHi!(j=i/2) (2)
In the synthesis unit 110, the sample interval of the signals XLj!, XHj! from the splitting unit 100 is doubled, at the same time that a sample having a zero value at a center position is inserted, as shown by the equations 3 and 4: ##EQU1##
A synthesis LPF 112L and a synthesis HPF 112H are an LPF and an HPF for band synthesis and interpolate output signals of the upsampling units 111.sub.L, 111.sub.H for regenerating signals XLi!, XUi! of the respective frequency bands. The band signals XLi!, XHi! are summed together by an adder 113 for synthesis for restoring the input signal xi!.
It should be noted that the analysis LPF 101.sub.L and the analysis HPF 101.sub.H of the splitting unit 100 and the synthesis LPF 112.sub.L and the synthesis HPF 112.sub.H of the synthesis unit 110 are constructed for completely or approximately satisfying the relation of the equations 5 and 6: EQU H.sub.0 (-z)F.sub.0 (z)+H.sub.1 (-z)F.sub.1 (z)=0 (5) EQU H.sub.0 (z)F.sub.0 (z)+H.sub.1 (z)F.sub.1 (z)=2z.sup.-L ( 6)
It is noted that H.sub.0 (z), H.sub.1 (z), F.sub.0 (z), F.sub.1 (z) are transfer functions of the analysis LPF 101.sub.L, analysis HPF 101.sub.H, synthesis LPF 112.sub.L and the synthesis HPF 112.sub.H, respectively. L is an arbitrary integer. By this constraint condition, it is assured that the output signal X"i! in the synthesis unit 110 from the adder 113 be completely or approximately coincident with the input signal xi!. If the above-described splitting and synthesis by wavelet transform are used for encoding, encoding/decoding is carried out between the downsampling units 102.sub.L, 102.sub.H and the upsampling units 111.sub.L, 111.sub.H. Although the input signal is split in the example of FIG. 1 into two frequency bands, the respective frequency bands are further recursively split twice or thrice for encoding for more efficient data compression.
FIG. 2 shows the structure of a conventional encoder 120 employing sub-band encoding. In the encoder 120, the input signal xi! is split by first-stage analysis LPF 121.sub.L and analysis HPF 121.sub.H into a low-frequency band signal XL.sub.0 i! and a high-frequency band signal XH.sub.0 i!. The low-frequency band signal XL.sub.0 j!, obtained by the down-sampling unit 122.sub.L by downsampling in accordance with the equation 1, is further split in frequency by a second-stage analysis LPF 123.sub.L and analysis HPF 123.sub.H. The resulting signals XL.sub.1 j!, XH.sub.1 j! are downsampled by downsampling units 124.sub.L, 124.sub.H, respectively, for generating a low frequency band signal XL.sub.1 k! and a high frequency band signal XH.sub.1 k!.
On the other hand, the high frequency band signal XH.sub.0 i!, which has passed through the first-stage analysis HPF 121.sub.H, is downsampled by the downsampling unit 122.sub.H. The resulting high-frequency band signal XH.sub.0 j! enters a delay unit 125 for synchronization with the low-frequency band signal XL.sub.0 j!. The low frequency range signal XL.sub.1 k! and the high frequency band signal XH.sub.1 k!, downsampled by the second-stage downsampling units 124.sub.L, 124.sub.H, and the first-stage high-frequency band signal XH.sub.0 j! appropriately delayed by the delay unit 125, enter quantizers 126a, 126b and 126c, respectively, for quantization with quantization steps QL.sub.1, QH.sub.1 and QH.sub.0, respectively, in accordance with the equations 7, 8 and 9: EQU XL.sub.1 'k!=XL.sub.1 k!/QL.sub.1 ( 7) EQU XH.sub.1 'k!=XH.sub.1 k!/QH.sub.1 ( 8) EQU XH.sub.0 'j!=XH.sub.0 j!/QH.sub.0 ( 9)
The quantization steps QL.sub.1, QH.sub.1 and QH.sub.0, are adaptively set in view of, for example, the amount of generated data, data speed on the transmission route or the recording capacity of the recording medium. In general, the quantization step is set so as to be narrower in a direction towards the lower frequency for prohibiting the lowering of the picture quality.
The quantized signals XL.sub.1 'k!, XH.sub.1 'k! and XH.sub.0 'j! enter a reversible encoding/multiplexing unit 127 for reversible encoding, such as Huffman encoding or arithmetic encoding, and multiplexing, before being outputted to a recording medium or to a transmission route, not shown.
FIG. 3 shows the structure of a conventional decoder 130 employing sub-band coding. The decoder 130 has a demultiplexer/reversible decoding unit 131 performing decoding which is a reversed operation with respect to the multiplexing and reversible encoding performed by the encoder 120 for restoring the signals XL.sub.1 'k!, XH.sub.1 'k! and XH.sub.0 'j!. These signals enter dequantizers 132a, 132b, 132c having respective different quantization steps so as to be transformed in accordance with the equations 10, 11 and 12: EQU XL.sub.1 "k!=XL.sub.1 'k!/QL.sub.1 ( 10) EQU XH.sub.1 "k!=XH.sub.1 'k!/QH.sub.1 ( 11) EQU XH0"j!=XH.sub.0 'j!/QH.sub.0 ( 12)
Of the outputs XL.sub.1 "k!, XH.sub.1 "k! and XH.sub.0 "k! of the dequantizers 132a, 132b, 132c, the low frequency band signal XL.sub.1 "k! and the high frequency band signal XH.sub.1 "k! for the second-stage spectrum splitting of the encoder 120 enter upsampling units 133.sub.L, 133.sub.H, respectively. The signals obtained by upsampling similar to that performed by the upsampling units 133.sub.L, 133.sub.H in accordance with the equations 3 and 4, respectively, enter a synthesis LPF 134.sub.L and a synthesis HPF 134.sub.H related with the synthesis LPF 123.sub.L and the synthesis HPF 123.sub.H, respectively, in accordance with the equations 5 and 6, respectively. The low frequency band signal XL.sub.1 "j!, XH.sub.1 "j! regenerated by the interpolation by the filters 134.sub.L, 134.sub.H, respectively, are summed together by an adder 135 to give a low frequency band signal XL.sub.0 "j! associated with the low frequency band signal XL.sub.0 j! obtained by first-stage spectrum splitting in the encoder 120.
On the other hand, the high frequency band signal XH.sub.0 "j!, associated with the first stage spectrum splitting of the first encoder 120, enters a delay unit 136, so as to be delayed by time necessary for reconstructing the low frequency band signal XL.sub.0 "j!, associated with the first stage spectrum splitting.
The low frequency band signal XL.sub.0 "j!, associated with the first stage spectrum splitting, and the high frequency band signal XH.sub.0 "j!, associated with the first stage spectrum splitting, delayed by the delay unit 136, enter upsampling units 137.sub.L, 137.sub.H, for upsampling, and are then interpolated by a synthesis LPF 138.sub.L and a synthesis HPF 138.sub.H for interpolation. The resulting low frequency band signal XL.sub.0 "i! and high frequency band signal XH.sub.0 "i! are summed together by an adder 139 to produce a regenerated signal x"i! corresponding to the input signal xi!.
In the conventional encoding method based on sub-band coding or wavelet transform, if a finite impulse response filter (FIR) having a large number of taps is used for frequency splitting, the range of ripple generation in the filter inhibiting area becomes wider such that ringing is produced around a picture portion exhibiting significant level changes, such as picture edges. In particular, if spectrum splitting is recursively performed a plurality of number of times, the number of filter taps is relatively increased with an increased number of times of spectrum splitting, as a result of which ringing is produced in a wide range around the picture edge.
Meanwhile, the range of generation of ringing can be decreased by using a filter having a smaller number of taps. However, in such case, the problem is raised that, due to deterioration of low frequency components, step-like changes are produced in the smoothly changing picture portions. This phenomenon is perceived in the picture as block distortion thus increasing deterioration in the picture quality. This problem is raised because the condition for complete reconstruction cannot be met due to quantization of the band-split signal such that aliasing produced on the high-pass filter side and that produced on the low-pass filter side cannot cancel each other. Although there is the problem of aliasing on the high pass filter side, mainly the aliasing on the low pass filter side involves problems since the high range side signals are deteriorated as compared to the low range side signals in encoding. This effect presents itself as ringing in the vicinity of the edge portion where the large level difference exists. In this case, the high range side signal contained by the picture edge is deteriorated such that aliasing on the low pass filter side cannot be canceled. If a filter having a long impulse response time duration is used, a picture area centered about the edge and having a length equal to the edge length is affected, thus causing deterioration of the high frequency components. If a filter having a short impulse response time duration is used, the range of generation of ringing is diminished, however, the passband on the filter frequency area becomes wider thus elongating the passband of the high pass filter towards the low frequency side. That is, deterioration on the high frequency side affects the low-frequency components, thus producing a block-like noise in the smoothly changing picture area. That is, low frequency components are deteriorated.
Briefly, the above problem is that of trade-off between the time domain and the frequency domain in the indeterminacy principle, such that, if resolution in the time domain is raised, that is the frequency domain is lowered.
The number of taps in a low-pass filter or a high-pass filter corresponds to duration in the time domain, so that, if the duration is shorter, that is if time resolution is higher, the resolution in the frequency domain is lowered, thus demonstrating the aliasing effect.
Moreover, the aliasing is produced by downsampling following filtering, such that aliasing is produced at the time point of downsampling following the filtering for spectrum splitting. If synthesis is performed without quantization, aliasing contained in the passbands of the low-pass filter and the high-pass filter should theoretically be canceled. However, since quantization is done for signal compression, aliasing cannot be canceled by synthesis.
Meanwhile, the number of filter taps means the number of filter coefficients or the length or span of a filter. The large number of filter taps is synonymous with the long length or span of the filter.